What is ln(7/(5x^5y)) ?

The solution to ln(7/(5x^5y)) is ln(7)-ln(5)-5ln(x)-ln(y)

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simplify ln(7/(5x^5y))

simplify

ln (\frac{7}{5 x ^{5} y})

ln (7) - ln (5) - 5 ln (x) - ln (y)

Solution steps

ln (\frac{7}{5 x ^{5} y})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{7}{5 x ^{5} y}) = ln (7) - ln (5 x^{5} y)

= ln (7) - ln (5 x^{5} y)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (5 x^{5} y) = ln (5) + ln (x^{5}) + ln (y)

= ln (7) - (ln (x^{5}) + ln (y) + ln (5))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (x^{5}) = 5 ln (x)

= ln (7) - (ln (5) + 5 ln (x) + ln (y))

- (ln (5) + 5 ln (x) + ln (y)) : - ln (5) - 5 ln (x) - ln (y)

= ln (7) - ln (5) - 5 ln (x) - ln (y)

3 lo g_{10} (x + 1) + lo g_{10} (4 x + 7)

lo g_{10} (\frac{7 a}{8})

lo g_{3} (1 2^{\frac{5}{6}}) x^{9}

lo g_{5} (\frac{x}{125})

ln (\frac{e ^{5}}{4})

What is ln(7/(5x^5y)) ?
The solution to ln(7/(5x^5y)) is ln(7)-ln(5)-5ln(x)-ln(y)